The disclosure relates to a system and methods for wrapping bales in a harvester that uses wrapping material stored in flat, folded layers instead of conventional round tubes or rolls, the system comprising: a material support tray, capable of supporting at least one bundle of wrapping material, at least one feed roll, and at least a first tensioning element, positioned adjacent to or in the material support tray and in operable contact with at least one bundle of wrapping material.